The question consists of four statements numbered “I, II, III and IV” given below it. You have to decide that the data provided in which of the statement(s) alone is/are sufficient to answer the question. ‘A’ and ‘B’ started a business where ‘B’ invested Rs. 1,800 more than ‘A’. ‘B’ invested for a time period that is 5 months less than the time period for which ‘A’ invested. Find the profit share of ‘B’. Statement I: ‘A’ invested for total of 10 months and the total annual profit earned from the business was Rs. 8,800. Statement II: If ‘B’ had invested Rs. 600 less, then the profit share of ‘A’ would have been 25% more than that of ‘B’ while the total annual profit earned from the business was Rs. 8,800. Statement III: The ratio of investment of ‘A’ and ‘B’ is 3:5, respectively. If ‘B’ had invested for 3 more months, then ratio of profit shares of ‘A’ to that of ‘B’ would be 3:4. Actual annual profit earned from the business was Rs. 8,800. Statement IV: ‘A’ had invested Rs. 2,700 for 10 months. Profit share of ‘A’ was Rs. 800 more than that of ‘B’.

Let the investment of ‘A’ = Rs. ‘X’ Then, investment of ‘B’ = Rs. (X + 1800) Let the time period of investment of ‘A’ = ‘y’ months Then, time period of investment of ‘B’ = (y – 5) months Statement I: We have, y = 10 So, ratio of profit shares of ‘A’ and ‘B’ = (X × 10):{(X + 1800) × (10 – 5)} = 10X:(5X + 9000) But we cannot proceed any further with this and we cannot determine the profit share of ‘B’. So, data in statement I alone is not sufficient to answer the question. Statement II: Reduced investment of ‘B’ = X + 1800 – 600 = Rs. (X + 1200) Ratio of profit shares of ‘A’ and ‘B’ respectively = (X × y):{(X + 1200) × (y – 5)} Or, Xy:{Xy + 1200y – 5X – 6000} According to the statement, Xy = 1.25 × (Xy + 1200y – 5X – 6000) Or, Xy = 1.25Xy + 1500y – 6.25X – 7500 Or, 0.25Xy + 1500y – 6.25X – 7500 = 0 Since this equation cannot be solved any further, we cannot determine the profit share of ‘B’. So, data in statement II alone is not sufficient to answer the question. Statement III: Let the investments of ‘A’ and ‘B’ be Rs. ‘3x’ and Rs. ‘5x’, respectively. Then, according to the statement, (3x × y):{5x × (y – 5 + 3)} = 3:4 Or, 3xy:{5x × (y – 2)} = 3:4 Or, 3xy:(5xy – 10x) = 3:4 Or, (3xy/3) = (5xy – 10x) ÷ 4 Or, 4xy = 5xy – 10x So, y = 10 So, ratio of actual profit shares of ‘A’ and ‘B’ = (3x × 10):{5x × (10 – 5)} = 30x:25x = 6:5 So, profit share of ‘B’ = 8800 × (5/11) = Rs. 4,000 So, data in statement III alone is sufficient to answer the question. Statement IV: Since ‘A’ has invested for 10 months, so time period of investment of ‘B’ = 10 – 5 = 5 months Investment of ‘B’ = 2700 + 1800 = Rs. 4,500 So, ratio of profit shares of ‘A’ and ‘B’ respectively = (2700 × 10):(4500 × 5) = 27000:22500 = 6:5 So, let the profit shares of ‘A’ and ‘B’ be Rs. 6k and Rs. 5k, respectively. We have, 6k – 5k = 800 Or, k = 800 So, profit share of ‘B’ = 5k = 800 × 5 = Rs. 4,000 So, data in statement IV alone is sufficient to answer the question. Hence, option C.